1. ## Probability problem

I would appreciate if you can solve this. Thank you.

A radio station in central Pennsylvania is having a birthday contest. One of the 366 days of the year is randomly selected with equal probability. If the month of a contestant's birthday matches the month selected - or the day of the month of the contestant's birthday matches the day of the month selected - or both - the contestant wins a compact disc. Otherwise, the contestant wins nothing. What is the probability that a contestant with a December 31 birthday will win? Express your answer as a common fraction.

2. Hi chil2e,

In a 366-day year, if each day is equally likely of being selected,

then the probability of a December day being selected is $\displaystyle \frac{31}{366}$.

The probability of the daydate 31 being selected is $\displaystyle \frac{7}{366}$.

If we sum the probabilities and subtract the overlapping day, Dec 31,
due to double-counting, we will have the probability that a contestant
with a Dec 31 birthday will win.

This is $\displaystyle \frac{31}{366}+\frac{7}{366}-\frac{1}{366}$